(2x-1)x(3x+4)=

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Solution for (2x-1)x(3x+4)= equation: 


Simplifying
(2x + -1) * x(3x + 4) = 0

Reorder the terms:
(-1 + 2x) * x(3x + 4) = 0

Reorder the terms:
(-1 + 2x) * x(4 + 3x) = 0

Reorder the terms for easier multiplication:
x(-1 + 2x)(4 + 3x) = 0

Multiply (-1 + 2x) * (4 + 3x)
x(-1(4 + 3x) + 2x * (4 + 3x)) = 0
x((4 * -1 + 3x * -1) + 2x * (4 + 3x)) = 0
x((-4 + -3x) + 2x * (4 + 3x)) = 0
x(-4 + -3x + (4 * 2x + 3x * 2x)) = 0
x(-4 + -3x + (8x + 6x2)) = 0

Combine like terms: -3x + 8x = 5x
x(-4 + 5x + 6x2) = 0
(-4 * x + 5x * x + 6x2 * x) = 0
(-4x + 5x2 + 6x3) = 0

Solving
-4x + 5x2 + 6x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-4 + 5x + 6x2) = 0

Factor a trinomial.
x((-4 + -3x)(1 + -2x)) = 0


Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

Move all terms containing x to the left, all other terms to the right.

Simplifying
x = 0

Subproblem 2
Set the factor '(-4 + -3x)' equal to zero and attempt to solve:

Simplifying
-4 + -3x = 0

Solving
-4 + -3x = 0

Move all terms containing x to the left, all other terms to the right.

Add '4' to each side of the equation.
-4 + 4 + -3x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -3x = 0 + 4
-3x = 0 + 4

Combine like terms: 0 + 4 = 4
-3x = 4

Divide each side by '-3'.
x = -1.333333333

Simplifying
x = -1.333333333

Subproblem 3
Set the factor '(1 + -2x)' equal to zero and attempt to solve:

Simplifying
1 + -2x = 0

Solving
1 + -2x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + -2x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2x = 0 + -1
-2x = 0 + -1

Combine like terms: 0 + -1 = -1
-2x = -1

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5
Solution
x = {0, -1.333333333, 0.5}

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